Yes, you are right S L, a direct brute force summation is surely not the most efficient method of determining the sums of these series. You are the only one so far with a valid solution that met the 50*eps tests. In fact your answers are very much closer than that to mine, within a few eps. However, there is another single analytic function that can be used which is much simpler and would undoubtedly give you a lower "size" than 92 if you or others can find it. R. Stafford

I am pleased that you solved this problem, David. Congratulations! I didn't find any particularly easier way of solving it. The crucial step is showing that the probability density is proportional to your 1/y^3 for points within the corresponding "kite-shaped region". I used the Jacobian between two coordinate systems to show that. After dividing that region into two halves everything falls into place, though in my dotage I had to make heavy use of the Symbolic Toolbox to check for errors. (I hope this problem will serve as a warning to people who recommend this method of producing random numbers with a predetermined sum.) R. Stafford

It is inherent in the definition of P here that the density, dP/dA, must increase as P increases and therefore dA/dP must decrease. In your proposed solution you have dA/dP increasing as P increases. R. Stafford